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Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
doctrine_n according_a find_v great_a 311 4 2.0768 3 false
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A61244 Mathematical collections and translations ... by Thomas Salusbury, Esq. Salusbury, Thomas. 1661 (1661) Wing S517; ESTC R19153 646,791 680

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a_o very_a exact_a observation_n and_o of_o great_a consequence_n we_o be_v advertise_v to_o make_v the_o observation_n of_o that_o concourse_n in_o the_o act_n of_o the_o same_o or_o just_o such_o another_o operation_n but_o in_o this_o our_o case_n wherein_o we_o be_v to_o show_v the_o error_n of_o astronomer_n this_o accurateness_n be_v not_o necessary_a for_o though_o we_o shall_v in_o favour_n of_o the_o contrary_a party_n suppose_v the_o say_a concourse_n to_o be_v make_v upon_o the_o pupil_n itself_o it_o will_v import_v little_a their_o mistake_n be_v so_o great_a i_o be_o not_o certain_a sagredus_fw-la that_o this_o will_v have_v be_v your_o objection_n sagr._fw-la it_o be_v the_o very_a same_o and_o i_o be_o glad_a that_o it_o be_v not_o altogether_o without_o reason_n as_o your_o concurrence_n in_o the_o same_o assure_v i_o but_o yet_o upon_o this_o occasion_n i_o will_v willing_o hear_v what_o way_n may_v be_v take_v to_o find_v out_o the_o distance_n of_o the_o concourse_n 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aestival_n winter_n and_o that_o the_o star_n do_v not_o rise_v and_o set_v to_o the_o earth_n but_o the_o earth_n to_o the_o star_n and_o that_o the_o east_n begin_v in_o the_o west_n and_o the_o west_n in_o the_o east_n and_o in_o a_o word_n that_o almost_o the_o whole_a course_n of_o the_o world_n be_v invert_v salv_n every_o thing_n please_v i_o except_o it_o be_v his_o have_v intermix_v place_n out_o of_o the_o sacred_a scripture_n always_o venerable_a and_o to_o be_v revere_v among_o these_o but_o two_o scurrilous_a foolery_n and_o attempt_v to_o wound_v with_o holy_a weapon_n those_o who_o philosophating_a in_o jest_n and_o for_o divertisement_n neither_o affirm_v nor_o deny_v but_o some_o presupposal_n and_o position_n be_v assume_v do_v familiar_o argue_v simp_n truth_n be_v he_o have_v displease_v i_o also_o and_o that_o not_o a_o little_a and_o especial_o by_o add_v present_o after_o that_o howbeit_o the_o copernichist_n answer_v though_o but_o very_o impertinent_o to_o 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simp_n i_o concur_v with_o
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without_o any_o cause_n against_o another_o man_n that_o have_v no_o other_o interest_n in_o copernicus_n but_o only_o as_o he_o be_v a_o approver_n of_o his_o doctrine_n now_o in_o regard_n of_o these_o false_a aspersion_n which_o they_o so_o unjust_o seek_v to_o throw_v upon_o i_o i_o have_v think_v it_o necessary_a for_o my_o justification_n before_o the_o world_n of_o who_o judgement_n in_o matter_n of_o religion_n and_o reputation_n i_o ought_v to_o make_v great_a esteem_n to_o discourse_v concern_v those_o particular_n which_o these_o man_n produce_v to_o scandalize_v and_o subvert_v this_o opinion_n and_o in_o a_o word_n to_o condemn_v it_o not_o only_o as_o false_a but_o also_o as_o heretical_a continual_o make_v a_o hipocritical_a zeal_n for_o religion_n their_o shield_n go_v about_o moreover_o to_o interest_n the_o sacred_a scripture_n in_o the_o dispute_n and_o to_o make_v they_o in_o a_o certain_a sense_n minister_n of_o their_o deceitful_a purpose_n and_o farthermore_o desire_v if_o i_o mistake_v not_o contrary_a to_o the_o intention_n of_o they_o and_o of_o the_o holy_a father_n to_o extend_v that_o i_o may_v not_o say_v abuse_n their_o authority_n so_o as_o that_o even_o in_o conclusion_n mere_o natural_a and_o not_o the_o fide_fw-la they_o will_v have_v we_o altogether_o leave_v sense_n and_o demonstrative_a reason_n for_o some_o place_n of_o scripture_n which_o sometime_o under_o the_o apparent_a word_n may_v contain_v a_o different_a sense_n now_o i_o hope_v to_o show_v with_o how_o much_o great_a piety_n and_o religious_a zeal_n i_o proceed_v than_o they_o do_v in_o that_o i_o propose_v not_o that_o the_o book_n of_o copernicus_n be_v not_o to_o be_v condemn_v but_o that_o it_o be_v not_o to_o be_v condemn_v as_o they_o will_v have_v it_o without_o understand_v it_o hear_v it_o or_o so_o much_o as_o see_v it_o and_o especial_o he_o be_v a_o author_n that_o never_o treat_v of_o matter_n of_o religion_n or_o faith_n nor_o by_o reason_n any_o way_n depend_v on_o the_o authority_n of_o sacred_a scripture_n whereupon_o he_o may_v have_v erroneous_o interpret_v they_o but_o always_o insist_o upon_o natural_a conclusion_n belong_v to_o the_o celestial_a motion_n handle_v with_o astronomical_a and_o geometrical_a demonstration_n not_o that_o he_o have_v not_o a_o respect_n to_o the_o place_n of_o the_o sacred_a leave_n but_o because_o he_o know_v very_o well_o that_o his_o say_a doctrine_n be_v demonstrate_v it_o can_v not_o contradict_v the_o scripture_n right_o and_o according_a to_o their_o true_a meaning_n understand_v and_o therefore_o in_o the_o end_n of_o his_o epistle_n dedicatory_a speak_v to_o the_o pope_n he_o say_v thus_o ten●●_n if_o there_o shall_v chance_v to_o be_v any_o mataeologist_n who_o though_o ignorant_a in_o all_o the_o mathematics_n yet_o pretend_v a_o skill_n in_o those_o learning_n shall_v dare_v upon_o the_o authority_n of_o some_o place_n of_o scripture_n wrest_v to_o their_o purpose_n to_o condemn_v and_o censure_v this_o my_o hypothesis_n i_o value_v they_o not_o but_o shall_v slight_v their_o inconsiderate_a judgement_n for_o it_o be_v not_o unknown_a that_o lactantius_n otherwise_o a_o famous_a author_n though_o mean_a mathematician_n write_v very_o childish_o touch_v the_o form_n of_o the_o earth_n when_o he_o scoff_v at_o those_o who_o affirm_v the_o earth_n to_o be_v in_o form_n of_o a_o globe_n so_o that_o it_o ought_v not_o to_o seem_v strange_a to_o the_o ingenious_a if_o any_o such_o shall_v likewise_o now_o deride_v we_o the_o mathematics_n be_v write_v for_o mathematician_n to_o who_o if_o i_o deceive_v not_o myself_o these_o labour_n of_o i_o shall_v seem_v to_o add_v something_o as_o also_o to_o the_o commonweal_n of_o the_o church_n who_o government_n be_v now_o in_o the_o hand_n of_o your_o holiness_n and_o of_o this_o kind_n do_v these_o appear_v to_o be_v who_o endeavour_n to_o persuade_v that_o copernicus_n may_v be_v condemn_v before_o his_o book_n be_v read_v and_o to_o make_v the_o world_n believe_v that_o it_o be_v not_o only_o lawful_a but_o commendable_a so_o to_o do_v produce_v certain_a authority_n of_o the_o scripture_n of_o divine_n and_o of_o council_n which_o as_o they_o be_v by_o i_o have_v in_o reverence_n and_o hold_v of_o supreme_a authority_n insomuch_o that_o i_o shall_v esteem_v it_o high_a temerity_n for_o any_o one_o to_o contradict_v they_o whilst_o they_o be_v use_v according_a to_o the_o in_o stitute_n of_o holy_a church_n so_o i_o believe_v that_o it_o be_v no_o error_n to_o speak_v so_o long_o as_o one_o have_v reason_n to_o suspect_v that_o a_o person_n have_v a_o desire_n for_o some_o concern_v of_o his_o own_o to_o produce_v and_o allege_v they_o to_o purpose_n different_a from_o those_o that_o be_v in_o the_o most_o sacred_a intention_n of_o the_o holy_a church_n therefore_o i_o not_o only_o protest_v and_o my_o sincerity_n shall_v manifest_v it_o self_n that_o i_o intend_v to_o submit_v myself_o free_o to_o renounce_v
by_o age_n or_o consume_v by_o worm_n nor_o sway_n and_o lean_a to_o this_o or_o that_o side_n that_o the_o seat_n and_o nest_n of_o live_a creature_n be_v not_o molest_v that_o the_o mountain_n and_o shore_n stand_v immovable_a against_o the_o violence_n of_o the_o wind_n and_o wave_n as_o they_o be_v at_o the_o beginning_n but_o the_o psalmist_n add_v a_o most_o elegant_a hypothesis_n of_o the_o separation_n of_o the_o water_n from_o the_o continent_n or_o main-land_n and_o adorn_v it_o with_o the_o production_n of_o fountain_n and_o the_o benefit_n that_o spring_n and_o rock_n exhibit_v to_o bird_n and_o beast_n nor_o do_v he_o omit_v the_o apparel_v the_o earth_n surface_n mention_v by_o moses_n among_o the_o work_n of_o the_o three_o day_n but_o more_o sublime_o describe_v it_o in_o his_o case_n in_o expression_n infuse_v from_o divine_a inspiration_n and_o flourish_v out_o the_o commemoration_n of_o the_o many_o commodity_n which_o redound_v from_o that_o exornation_n for_o the_o nourishment_n and_o comfort_n of_o man_n and_o shelter_n covert_a of_o beast_n the_o four_o part_n begin_v at_o verse_n 20._o celebrate_v the_o four_o day_n work_n viz._n the_o sun_n and_o moon_n but_o chief_o the_o commodiousness_n of_o those_o thing_n which_o in_o their_o season_n befall_v to_o all_o live_a creature_n and_o to_o man_n this_o be_v the_o subject_a matter_n of_o his_o discourse_n so_o that_o it_o plain_o appear_v he_o act_v not_o the_o part_n of_o a_o astronomer_n for_o if_o he_o have_v he_o will_v not_o then_o have_v omit_v to_o mention_v the_o five_o planet_n than_o who_o moiton_n nothing_o be_v more_o admirable_a nothing_o more_o excellent_a nothing_o that_o can_v more_o evident_o set_v forth_o the_o wisdom_n of_o the_o creator_n among_o the_o learned_a the_o five_o part_n begin_v verse_n 25._o with_o the_o five_o day_n work_n and_o it_o store_v the_o sea_n with_o fish_n and_o cover_v they_o with_o ship_n the_o six_o part_n be_v more_o obscure_o hint_v at_o verse_n 28._o and_o allude_v to_o the_o land-creature_n that_o be_v create_v the_o six_o day_n and_o last_o he_o declare_v the_o goodness_n of_o god_n in_o general_n who_o daily_o creat_v and_o preserve_v all_o thing_n so_o that_o whatever_o he_o say_v of_o the_o world_n be_v in_o relation_n to_o live_v creature_n he_o speak_v of_o nothing_o but_o what_o be_v grant_v on_o all_o hand_n for_o that_o it_o be_v his_o intent_n to_o extol_v thing_n know_v and_o not_o to_o dive_v into_o hide_a matter_n but_o to_o invite_v man_n to_o contemplate_v the_o benefit_n that_o redound_v unto_o they_o from_o the_o work_n of_o each_o of_o these_o day_n and_o i_o do_v also_o beseech_v my_o reader_n not_o forget_v the_o divine_a goodness_n confer_v on_o mankind_n the_o consideration_n of_o which_o the_o psalmist_n do_v chief_o urge_v that_o when_o he_o return_v from_o the_o temple_n and_o enter_v into_o the_o school_n of_o astronomy_n he_o will_v with_o i_o praise_v and_o admire_v the_o wisdom_n and_o greatness_n of_o the_o creator_n which_o i_o discover_v to_o he_o by_o a_o more_o narrow_a explication_n of_o the_o world_n form_n the_o disquisition_n of_o cause_n and_o detection_n of_o the_o error_n of_o sight_n and_o so_o he_o will_v not_o only_o extol_v the_o bounty_n of_o god_n in_o the_o preservation_n of_o live_v creature_n of_o all_o kind_n and_o establishment_n of_o the_o earth_n but_o even_o in_o its_o motion_n also_o which_o be_v so_o strange_a so_o admirable_a he_o will_v acknowledge_v the_o wisdom_n of_o the_o creator_n but_o he_o who_o be_v so_o stupid_a as_o not_o to_o comprehend_v the_o science_n of_o astronomy_n or_o so_o weak_a and_o scrupulous_a as_o to_o think_v it_o a_o offence_n of_o piety_n to_o adhere_v to_o copernicus_n he_o i_o advise_v that_o leave_v the_o study_n of_o astronomy_n and_o censure_v the_o opinion_n of_o philosopher_n at_o pleasure_n he_o betake_v himself_o to_o his_o own_o concern_v and_o that_o desist_v from_o further_a pursuit_n of_o these_o intricate_a study_n he_o keep_v at_o home_n and_o manure_v his_o own_o ground_n and_o with_o those_o eye_n wherewith_o alone_o he_o see_v be_v elevate_v towards_o this_o to_o be_v admire_v heaven_n let_v he_o pour_v forth_o his_o whole_a heart_n in_o thanks_o and_o praise_n to_o god_n the_o creator_n and_o assure_v himself_o that_o he_o shall_v therein_o perform_v as_o much_o worship_n to_o god_n as_o the_o astronomer_n on_o who_o god_n have_v bestow_v this_o gift_n that_o though_o he_o see_v more_o clear_o with_o the_o eye_n of_o his_o understanding_n yet_o whatever_o he_o have_v attain_v to_o he_o be_v both_o able_a and_o willing_a to_o extol_v his_o god_n above_o it_o and_o thus_o much_o concern_v the_o authority_n of_o sacred_a scripture_n now_o as_o touch_v the_o opinion_n of_o the_o saint_n about_o these_o natural_a point_n i_o answer_v in_o one_o word_n that_o in_o theology_n the_o weight_n of_o authority_n but_o in_o philosophy_n the_o weight_n of_o reason_n be_v to_o be_v consider_v therefore_o sacred_a be_v lactantius_n who_o deny_v the_o earth_n rotundity_n sacred_a be_v augustine_n who_o grant_v the_o earth_n to_o be_v round_o but_o deny_v the_o antipode_n sacred_a be_v the_o officium_fw-la liturgy_n of_o our_o modern_n who_o admit_v the_o smallnesse_n of_o the_o earth_n but_o deny_v its_o motion_n but_o to_o i_o more_o sacred_a than_o all_o these_o be_v truth_n who_o with_o respect_n to_o the_o doctor_n of_o the_o church_n do_v demonstrate_v from_o philosophy_n that_o the_o earth_n be_v both_o round_a circumhabit_v by_o antipode_n of_o a_o most_o contemptible_a smallness_n and_o in_o a_o word_n that_o it_o be_v rank_v among_o the_o planet_n a_o abstract_n of_o some_o passage_n in_o the_o commentary_n of_o didacus_n à_fw-la stunica_fw-la of_o salamanca_n upon_o job_n the_o toledo_n edition_n print_v by_o john_n roderick_n anno_fw-la 1584._o in_o quarto_n pag._n 205._o &_o seqq_fw-la on_o these_o word_n chap._n 9_o verse_n 6._o who_o shake_v the_o earth_n out_o of_o her_o place_n and_o the_o pillar_n thereof_o tremble_v the_o sacred_a penman_n here_o set_v down_o another_o effect_n whereby_o god_n show_v his_o almighty_a power_n join_v with_o infinite_a wisdom_n which_o place_n though_o it_o must_v be_v confess_v very_o difficult_a to_o understand_v may_v be_v great_o clear_v by_o the_o opinion_n of_o the_o pythagorian_n who_o hold_v the_o earth_n to_o be_v move_v of_o its_o own_o nature_n and_o that_o the_o motion_n of_o the_o star_n can_v no_o other_o way_n be_v ascertain_v they_o be_v so_o extreme_o different_a in_o tardity_n and_o velocity_n of_o which_o judgement_n be_v philolaus_n and_o heraclides_fw-la ponticus_n as_o plutarch_n relate_v in_o his_o book_n de_fw-fr placitis_fw-la philosophorum_fw-la who_o be_v follow_v by_o numa_n pompilius_n and_o which_o i_o more_o regard_n the_o divine_a plato_n in_o his_o old_a age_n insomuch_o that_o he_o affirm_v that_o it_o be_v most_o absurd_a to_o think_v otherwise_o as_o the_o same_o plutarch_n tell_v we_o in_o his_o ejus_fw-la numa_n and_o hypocrates_n in_o his_o book_n de_fw-fr flatibus_fw-la call_v the_o air_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d i._n e._n the_o earth_n chariot_n but_o in_o this_o our_o age_n copernicus_n do_v demonstrate_v the_o course_n of_o the_o blanet_n to_o be_v according_a to_o this_o opinion_n nor_o be_v it_o to_o be_v doubt_v but_o that_o the_o planet_n place_n may_v be_v more_o exact_o and_o certain_o assign_v by_o his_o doctrine_n than_o by_o ptolemy_n great_a almoge_v or_o systeme_n or_o the_o opinion_n of_o any_o other_o for_o its_o manifest_a that_o ptolemy_n can_v never_o describe_v either_o the_o motion_n of_o the_o equinox_n or_o assign_v the_o certain_a and_o positive_a beginning_n of_o the_o year_n the_o which_o he_o ingenious_o confess_v in_o lib._n 3._o de_fw-fr almage_a magnum_fw-la ch._n 2._o and_o which_o he_o leave_v to_o be_v discover_v in_o after_o time_n by_o those_o astronomer_n who_o come_v into_o the_o world_n much_o late_a than_o he_o may_v be_v able_a to_o invent_v some_o way_n to_o make_v more_o accurate_a observation_n and_o although_o the_o hypothesis_n alphonsine_n &_o thebith_n ben_n core_n have_v attempt_v to_o explain_v they_o yet_o it_o appear_v that_o they_o have_v do_v as_o much_o as_o nothing_o for_o the_o position_n of_o the_o alphonsine_n disagree_v among_o themselves_o as_o ricius_fw-la prove_v and_o although_o the_o reason_n of_o thebith_n be_v more_o acute_a and_o that_o thereby_o he_o determine_v the_o certain_a beginning_n of_o the_o year_n be_v that_o which_o ptolemy_n seek_v for_o yet_o it_o be_v now_o clear_a that_o the_o progression_n of_o the_o equinox_n be_v much_o long_a than_o he_o conceive_v they_o can_v be_v moreover_o the_o sun_n be_v find_v to_o be_v much_o near_a to_o we_o than_o it_o be_v hold_v to_o be_v in_o time_n past_a by_o above_o forty_o thousand_o foot_n
a_o philosopher_n determine_v the_o original_n of_o the_o nerve_n requisite_n to_o fit_a a_o man_n to_o philosophate_v well_o after_o the_o manner_n of_o aristotle_n a_o cunning_a way_n to_o gather_v philosophy_n out_o of_o any_o book_n whatsoever_o whatsoever_o a_o word_n signify_v work_n compose_v of_o many_o fragment_n of_o verse_n collect_v out_o of_o the_o poet_n invention_n of_o the_o telescope_n take_v from_o aristotle_n chemist_n interpret_v the_o fable_n of_o the_o poet_n to_o be_v secret_n for_o make_v of_o gold_n some_o of_o aristotle_n sectator_n impair_v the_o reputation_n of_o their_o master_n in_o go_v about_o to_o enhanse_v it_o a_o ridiculous_a passage_n of_o a_o certain_a statuary_n a_o brave_a resolution_n of_o a_o certain_a peripatetic_a philosopher_n the_o servile_a spirit_n of_o some_o of_o aristotle_n follower_n too_o close_o adhere_v to_o aristotle_n be_v unblamable_a it_o be_v not_o just_a that_o those_o who_o never_o philosophate_o shall_v ●surp_v the_o title_n of_o philosopher_n the_o sensible_a world_n the_o motion_n of_o the_o earth_n be_v imperceptible_a to_o its_o inhabitant_n the_o earth_n can_v have_v no_o other_o motion_n than_o those_o which_o to_o we_o appear_v common_a to_o all_o the_o rest_n of_o the_o universe_n the_o earth_n except_v the_o diurnal_a motion_n seem_v commune_v to_o all_o the_o universe_n save_v only_o the_o earth_n except_v aristotle_n and_o ptolemy_n argue_v against_o the_o diurnal_a motion_n attribute_v to_o the_o earth_n why_o the_o diurnal_a motion_n more_o probable_o shall_v belong_v to_o the_o earth_n than_o to_o the_o rest_n of_o the_o universe_n motion_n as_o to_o the_o thing_n that_o equal_o move_v thereby_o be_v as_o if_o it_o never_o be_v &_o so_o far_o operate_v as_o it_o have_v relation_n to_o thing_n deprive_v of_o motion_n a_o proposition_n take_v by_o aristotle_n from_o the_o ancient_n but_o somewhat_o alter_v by_o he_o the_o first_o discourse_n to_o prove_v that_o the_o diurnal_a motion_n belong_v to_o the_o earth_n nature_n never_o do_v that_o by_o many_o thing_n which_o may_v be_v do_v by_o a_o few_o the_o diurnal_a motion_n cause_v no_o mutation_n among_o the_o celestial_a body_n but_o all_o change_n have_v relation_n to_o the_o earth_n a_o second_o confirmation_n that_o the_o diurnal_a motion_n belong_v to_o the_o earth_n circular_a motion_n be_v not_o contrary_a according_a to_o aristotle_n aristotle_n as_o you_o see_v in_o a_o mill_n wherein_o the_o implicate_v clog_n set_v the_o wheel_n on_o move_v a_o three_o confirmation_n of_o the_o same_o doctrine_n the_o great_a orb_n make_v their_o conversion_n in_o great_a time_n the_o time_n of_o the_o medicean_n planet_n conversion_n the_o motion_n of_o 24_o hour_n ascribe_v to_o the_o high_a sphere_n disorder_v the_o period_n of_o the_o inferior_a the_o four_o confirmation_n great_a disparity_n among_o the_o motion_n of_o the_o particular_a fix_a star_n if_o their_o sphere_n be_v movable_a the_o five_o confirmation_n 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i_o shall_v think_v you_o will_v do_v more_o than_o i_o can_v for_o i_o profess_v i_o can_v comprehend_v these_o thing_n beside_o
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purpose_n to_o dispute_v and_o it_o be_v fit_a that_o every_o one_o shall_v move_v the_o difficulty_n that_o he_o met_n withal_o for_o this_o be_v the_o way_n to_o come_v to_o the_o knowledge_n of_o the_o truth_n therefore_o speak_v free_o sagr._fw-la if_o it_o be_v true_a that_o the_o impetus_fw-la wherewith_o the_o ship_n move_v do_v remain_v indelible_o impress_v in_o the_o stone_n after_o it_o be_v let_v fall_n from_o the_o mast_n and_o if_o it_o be_v far_a true_a that_o this_o motion_n bring_v no_o impediment_n or_o retardment_n to_o the_o motion_n direct_o downward_o natural_a to_o the_o stone_n project_n it_o be_v necessary_a that_o there_o do_v a_o effect_n ensue_v of_o a_o very_a wonderful_a nature_n let_v a_o ship_n be_v suppose_v to_o stand_v still_o and_o
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〈…〉_z that_o in_o case_n that_o motion_n shall_v not_o belong_v to_o the_o star_n it_o will_v be_v necessary_a to_o confess_v that_o the_o horizon_n with_o a_o contrary_a motion_n will_v go_v down_o and_o that_o consequent_o the_o earth_n will_v reoolve_v in_o itself_o a_o contrary_a way_n to_o that_o wherewith_o the_o star_n seem_v to_o move_v that_o be_v from_o west_n to_o east_n which_o be_v according_a to_o the_o order_n of_o the_o sign_n of_o the_o zodiac_n as_o in_o the_o next_o place_n to_o the_o other_o motion_n the_o sun_n be_v fix_v in_o the_o centre_n of_o the_o zodiac_n and_o the_o earth_n movable_a about_o its_o circumference_n to_o make_v the_o sun_n seem_v unto_o we_o to_o move_v about_o the_o say_a zodiac_n according_a to_o the_o order_n of_o the_o sign_n it_o be_v necessary_a that_o the_o earth_n move_v according_a to_o the_o same_o order_n to_o the_o end_n that_o the_o sun_n may_v seem_v to_o we_o to_o possess_v always_o that_o degree_n in_o the_o zodiac_n that_o be_v 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circumference_n of_o a_o circle_n 145_o a_o movable_a fall_n from_o the_o top_n of_o a_o tower_n move_v in_o the_o circumference_n of_o a_o circle_n 146_o a_o movable_a fall_n from_o a_o tower_n move_v neither_o more_o nor_o less_o then_o if_o it_o have_v stay_v always_o there_o 146_o a_o movable_a fall_n from_o a_o tower_n move_v with_o a_o uniform_a not_o a_o accelerate_v motion_n 146_o the_o cadent_a movable_n if_o it_o fall_v with_o a_o degree_n of_o velocity_n acquire_v in_o a_o like_a time_n with_o a_o vniform_a motion_n it_o shall_v pass_v a_o space_n double_a to_o that_o pass_v with_o the_o accelerate_v motion_n 202_o admirable_a problem_n of_o movable_n descend_v by_o the_o quadrant_n of_o a_o circle_n and_o those_o descend_v by_o all_o the_o chord_n of_o the_o whole_a circle_n 412_o mundane_a mundane_a body_n be_v move_v in_o the_o begin_n in_o a_o right_a line_n and_o afterward_o circular_o according_a of_o plato_n 11_o n_o natural_a that_o which_o be_v violent_a can_v be_v 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original_a of_o the_o nerve_n according_a to_o aristotle_n and_o according_a to_o physician_n 91_o the_o ridiculous_a answer_n of_o a_o philosopher_n determine_v the_o original_a of_o the_o nerve_n 91_o o_o object_n object_n the_o more_o vigorous_a they_o be_v in_o light_n the_o more_o they_o do_v seem_v to_o increase_v 305_o that_o remote_a object_n appear_v so_o small_a be_v the_o defect_n of_o the_o eye_n as_o be_v demonstrate_v 337_o in_o object_n far_o remote_a and_o luminous_a a_o small_a accession_n or_o recession_n be_v imperceptible_a 350_o opinion_n it_o be_v all_o one_o whether_o opinion_n be_v new_a to_o man_n or_o man_n new_a to_o opinion_n 77_o orbe_fw-la and_o orb_n the_o great_a orb_n make_v their_o conversion_n in_o great_a time_n 101_o &_o 331_o it_o be_v more_o rational_a that_o the_o orb_n contain_v and_o the_o part_n contain_v do_v move_v all_o about_o one_o centre_n than_o about_o divers_a 295_o p_o passion_n infinite_a passion_n be_v perhaps_o but_o one_o only_a 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paralogism_n of_o the_o say_v peripatetic_a who_o prove_v ignotum_fw-la per_fw-la ignotius_fw-la 183_o the_o discourse_n of_o peripatetic_n full_a of_o error_n and_o contradiction_n 376_o the_o peripatetic_n persecute_v galileo_n out_o of_o envy_n to_o his_o happy_a discovery_n in_o philosophy_n 427_o the_o peripatetic_n in_o defect_n of_o reason_n repair_v to_o scripture_n for_o argument_n against_o their_o adversary_n 429_o philosopher_n it_o be_v not_o just_a that_o those_o who_o never_o phylosophate_n shall_v usurp_v the_o title_n of_o philosopher_n 96_o philosophy_n the_o dispute_n and_o contradiction_n of_o philosopher_n may_v conduce_v to_o the_o benefit_n of_o philosophy_n 25_o a_o cunning_a way_n to_o gather_v philosophy_n out_o of_o any_o book_n whatsoever_o 92_o planet_n the_o approximation_n and_o recession_n of_o the_o three_o superior_a planet_n import_v double_v the_o sun_n distance_n 299_o the_o difference_n of_o the_o planet_n apparent_a magnitude_n less_o in_o 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do_v not_o oblige_v we_o to_o receive_v those_o precept_n which_o they_o have_v not_o so_o much_o as_o in_o their_o intention_n enjoin_v but_o if_o they_o do_v reflect_v and_o consider_v thereon_o they_o will_v long_o since_o have_v condemn_v it_o if_o they_o have_v judge_v it_o erroneous_a which_o we_o do_v not_o find_v that_o they_o have_v do_v nay_o after_o that_o some_o divine_n have_v begin_v to_o consider_v it_o we_o find_v that_o they_o have_v not_o deem_v it_o erroneous_a as_o we_o read_v in_o the_o commentary_n of_o didacus_n a_o stunica_fw-la upon_o job_n in_o cap._n 9_o v_o 6._o on_o the_o word_n qui_fw-la commovet_fw-la terram_fw-la de_fw-la loco_fw-la svo_fw-la etc._n etc._n where_o he_o at_o large_a discourse_v upon_o the_o copernican_n hypothesis_n and_o conclude_v that_o the_o mobility_n of_o the_o earth_n be_v not_o contrary_a to_o scripture_n withal_o i_o may_v just_o question_v the_o truth_n of_o that_o determination_n namely_o that_o the_o church_n enjoin_v we_o 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thrasimenus_n where_o hannibal_n give_v a_o fatal_a overthrow_n to_o the_o roman_a legion_n in_o that_o sweet_a and_o fertile_a part_n of_o happy_a italy_n call_v the_o territory_n of_o perugia_n a_o branch_n of_o the_o dukedom_n of_o tuscany_n which_o at_o present_a submit_v to_o the_o jurisdiction_n of_o the_o church_n as_o be_v a_o part_n of_o st._n peter_n patrimony_n his_o parent_n who_o be_v more_o zealous_a of_o the_o good_a of_o his_o soul_n than_o observant_a of_o the_o propension_n of_o his_o genius_n dedicate_v he_o according_a to_o the_o devotion_n of_o that_o country_n to_o the_o service_n of_o the_o church_n and_o enter_v he_o into_o the_o flourish_a order_n of_o blackfriar_n call_v from_o the_o place_n monk_n of_o monte_n casino_n and_o from_o the_o founder_n benedictines_n nature_n that_o she_o may_v consummate_v the_o profusion_n of_o her_o favour_n upon_o he_o send_v he_o into_o the_o world_n in_o a_o age_n that_o be_v so_o ennoble_v and_o illuminate_v with_o 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occasion_n detain_v he_o in_o romagna_n he_o perfect_v the_o first_o book_n of_o this_o his_o discourse_n concern_v the_o mensuration_n of_o run_v water_n he_o confess_v that_o he_o have_v some_o year_n before_o apply_v himself_o to_o this_o part_n of_o practical_a geometry_n and_o from_o several_a observation_n collect_v part_n of_o that_o doctrine_n which_o at_o this_o time_n he_o put_v into_o method_n and_o which_o have_v procure_v he_o the_o repute_n of_o so_o much_o skill_n that_o he_o begin_v to_o be_v court_v by_o sundry_a prince_n and_o great_a prelate_n in_o particular_a about_o the_o begin_n of_o the_o year_n 1623._o and_o before_o his_o invitation_n to_o rome_n he_o be_v employ_v by_o prince_n ferdinando_n i_o grand_a duke_n of_o tuscany_n to_o remedy_v the_o disorder_n which_o at_o that_o time_n happen_v in_o the_o valley_n of_o pisa_n in_o the_o meadow_n that_o lie_v upon_o the_o bank_n of_o serchio_n and_o fiume_n morto_n and_o in_o the_o presence_n of_o the_o grand_a duke_n grand_a duchess_n mother_n the_o commissioner_n of_o sewer_n and_o sundry_a other_o person_n in_o a_o few_o hour_n he_o make_v so_o great_a a_o progress_n in_o that_o affair_n as_o give_v his_o most_o serene_a highness_n high_a satisfaction_n and_o gain_v himself_o much_o honour_n §_o no_o soon_o have_v he_o in_o his_o forementioned_a voyage_n to_o romagna_n which_o be_v but_o few_o month_n after_o in_o the_o same_o year_n commit_v his_o conception_n to_o paper_n but_o he_o communicate_v they_o to_o certain_a of_o his_o friend_n in_o which_o number_n we_o find_v signore_v giampoli_n secretary_n of_o the_o pope_n private_a affair_n who_o in_o the_o begin_n of_o the_o first_o book_n he_o grateful_o acknowledge_v to_o have_v be_v contributory_a in_o his_o purse_n towards_o defray_v the_o charge_n of_o experiment_n and_o in_o his_o person_n towards_o the_o debate_n and_o complete_n of_o argument_n upon_o this_o subject_a some_o few_o year_n after_o the_o importunity_n of_o friend_n and_o the_o zeal_n he_o have_v for_o the_o public_a good_a prevail_v with_o he_o to_o present_v the_o world_n with_o his_o first_o discourse_n accompany_v with_o a_o treatise_n of_o the_o geometrical_a demonstration_n of_o his_o whole_a doctrine_n what_o reception_n it_o find_v with_o the_o judicious_a must_v needs_o be_v imagine_v by_o any_o one_o that_o have_v observe_v how_o novelty_n and_o facility_n in_o conjunction_n with_o verity_n make_v a_o charm_n of_o irresistible_a operation_n §_o new_o it_o be_v for_o that_o no_o man_n before_o he_o have_v ever_o attempt_v to_o demonstrate_v all_o the_o three_o dimension_n to_o wit_n the_o length_n breadth_n and_o profundity_n of_o this_o fluid_a and_o current_a element_n and_o he_o detect_v such_o gross_a error_n in_o those_o few_o that_o have_v untertook_v to_o write_v upon_o the_o subject_a of_o which_o he_o instance_v in_o frontinus_n and_o fontana_n as_o those_o that_o include_v the_o rest_n and_o deliver_v such_o singular_a and_o unheard_a of_o paradox_n for_o so_o they_o sound_v in_o vulgar_a ear_n as_o can_v but_o procure_v unspeakable_a delight_n to_o his_o reader_n §_o easie_n it_o be_v likewise_o and_o true_a and_o that_o upon_o so_o familiar_a experiment_n and_o manifest_a demonstration_n that_o i_o have_v oft_o question_v with_o myself_o which_o merit_v the_o great_a wonder_n he_o for_o discover_v or_o all_o man_n that_o handle_v the_o argument_n before_o he_o for_o not_o discover_v a_o doctrine_n of_o such_o strange_a facility_n and_o infallibility_n but_o yet_o as_o if_o our_o author_n design_v to_o oblige_v the_o whole_a world_n to_o he_o by_o so_o excellent_a a_o present_n he_o select_v a_o subject_a that_o he_o know_v will_v be_v carress_v by_o all_o person_n of_o noble_a soul_n upon_o the_o account_n afore-named_n and_o by_o all_o mankind_n in_o general_n as_o gratify_v they_o in_o their_o much_o adore_a idol_n utility_n and_o to_o render_v his_o art_n the_o more_o profitable_a he_o reduce_v the_o lofty_a and_o easy_a to-be-mistaken_a speculation_n of_o the_o theory_n into_o certain_a and_o facile_a direction_n for_o practice_n teach_v we_o how_o to_o prevent_v and_o repair_v the_o breach_n of_o sea_n and_o inundation_n of_o river_n to_o drain_v and_o recover_v fen_n and_o march_n to_o divert_v convey_v and_o distribute_v water_n for_o the_o flow_v and_o stercoration_n of_o ground_n strengthen_v of_o fortification_n serve_v of_o aquaduct_n preserve_v of_o health_n by_o cleanse_v street_n and_o scour_a sewer_n and_o maintain_v of_o commerce_n by_o defend_v bridge_n clear_n river_n and_o open_v pore_n and_o channel_n with_o innumerable_a other_o benefit_n of_o the_o like_a nature_n and_o that_o i_o may_v omit_v no_o circumstance_n that_o may_v recommend_v my_o author_n the_o fortune_n of_o this_o his_o treatise_n have_v be_v such_o that_o as_o if_o he_o intend_v a_o plus_fw-fr ultra_fw-la by_o it_o or_o as_o if_o all_o man_n despair_v to_o outdo_v it_o or_o last_o as_o if_o
ferara_n yet_o nevertheless_o from_o this_o particular_a doctrine_n well_o understand_v good_a judgement_n may_v be_v make_v of_o other_o the_o like_a case_n in_o general_n i_o say_v then_o for_o great_a perspecuity_n and_o better_a understanding_n of_o the_o whole_a that_o about_o thirteen_o mile_n above_o ferara_n near_o to_o stellata_fw-la the_o main_a of_o po_n branch_a itself_o into_o two_o part_n with_o one_o of_o its_o arm_n it_o come_v close_o to_o ferara_n retain_v the_o name_n of_o the_o po_n of_o ferara_n and_o here_o again_o it_o divide_v itself_o into_o two_o other_o branch_n and_o that_o which_o continue_v on_o the_o right_a hand_n be_v call_v the_o po_n of_o argenta_n and_o of_o primaro_n and_o that_o on_o the_o leave_v the_o po_n of_o volana_n but_o for_o that_o the_o bed_n of_o the_o po_n of_o ferara_n be_v heretofore_o augment_v and_o raise_v it_o follow_v that_o it_o rest_v whole_o deprive_v of_o the_o water_n of_o the_o great_a po_n except_o in_o the_o time_n of_o its_o great_a swell_n for_o in_o that_o case_n this_o po_n of_o ferara_n be_v restrain_v with_o a_o bank_n near_o to_o bondeno_n will_v come_v also_o in_o the_o overflowing_n of_o the_o main_a po_n to_o be_v free_a from_o its_o water_n but_o the_o lord_n of_o ferara_n be_v wont_n at_o such_o time_n as_o the_o po_n threaten_v to_o break_v out_o to_o cut_v the_o bank_n by_o which_o cut_v there_o disgorge_v such_o a_o torrent_n of_o water_n that_o it_o be_v observe_v that_o the_o main_a po_n in_o the_o space_n of_o some_o few_o hour_n abate_v near_o a_o foot_n and_o all_o person_n that_o i_o have_v speak_v with_o hitherto_o move_v by_o this_o experiment_n think_v that_o it_o be_v of_o great_a profit_n and_o benefit_n to_o keep_v ready_a this_o vent_n and_o to_o make_v use_n of_o it_o in_o the_o time_n of_o its_o fullness_n and_o indeed_o the_o thing_n consider_v simple_o and_o at_o the_o first_o appearance_n it_o seem_v that_o none_o can_v think_v otherwise_o the_o rather_o for_o that_o 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more_o to_o the_o purpose_n whole_o to_o stop_v it_o up_o than_o to_o maintain_v it_o open_a yet_o i_o be_o not_o so_o wed_v to_o my_o opinion_n but_o that_o i_o be_o ready_a to_o change_v my_o judgement_n upon_o strength_n of_o better_a reason_n especial_o of_o one_o that_o shall_v have_v first_o well_o understand_v the_o beginning_n of_o this_o my_o discourse_n which_o i_o frequent_o inculcate_v because_o it_o be_v absolute_o impossible_a without_o this_o advertisement_n to_o treat_v of_o these_o matter_n and_o not_o commit_v very_o great_a error_n i_o propose_v therefore_o to_o consideration_n that_o although_o it_o be_v true_a that_o whilst_o the_o water_n of_o the_o main_a po_n be_v at_o its_o great_a height_n the_o bank_n and_o dam_n then_o cut_v of_o the_o po_n of_o ferara_n and_o the_o superior_a water_n have_v a_o very_a great_a fall_n into_o the_o channel_n of_o ferara_n they_o precipitate_v into_o the_o same_o with_o great_a violence_n and_o velocity_n and_o with_o the_o same_o in_o the_o beginning_n or_o little_o less_o they_o run_v towards_o the_o po_n of_o volana_n and_o of_o argenta_n on_o the_o sea_n coast_n yet_o after_o the_o space_n of_o some_o few_o hour_n the_o po_n of_o ferara_n be_v full_a and_o the_o superior_a water_n not_o find_v so_o great_a a_o diclivity_n there_o as_o they_o have_v at_o the_o begin_n of_o the_o cut_n they_o fall_v not_o into_o the_o same_o with_o the_o former_a velocity_n but_o with_o far_o less_o and_o thereby_o a_o great_a deal_n less_o water_n begin_v to_o issue_v from_o the_o great_a po_n and_o if_o we_o diligent_o compare_v the_o velocity_n at_o the_o first_o cut_v with_o the_o velocity_n of_o the_o water_n after_o the_o cut_v make_v and_o when_o the_o po_n of_o ferara_n shall_v be_v full_a of_o water_n we_o shall_v find_v perhaps_o that_o to_o be_v fifteen_o or_o twenty_o time_n great_a than_o this_o and_o consequent_o the_o water_n which_o issue_v from_o the_o great_a po_n that_o first_o impetuosity_n be_v past_a shall_v be_v only_o the_o fifteen_o or_o twenty_o part_n of_o that_o which_o issue_v at_o the_o beginning_n and_o therefore_o the_o water_n of_o the_o main_a po_n will_v return_v in_o a_o small_a time_n almost_o to_o the_o first_o height_n and_o here_o i_o will_v pray_v those_o who_o rest_v not_o whole_o satisfy_v with_o what_o have_v be_v say_v that_o for_o the_o love_n of_o truth_n and_o the_o common_a good_a they_o will_v please_v to_o make_v diligent_a observation_n whether_o in_o the_o time_n of_o great_a flood_n the_o say_a bank_n or_o dam_n at_o bondeno_n be_v cut_v and_o that_o in_o few_o hour_n the_o main_a po_n diminish_v as_o have_v be_v say_v about_o a_o foot_n in_o its_o height_n that_o they_o will_v observe_v i_o say_v whether_o a_o day_n or_o two_o be_v past_a the_o water_n of_o the_o main_a po_n return_v almost_o to_o their_o first_o height_n for_o if_o this_o shall_v follow_v it_o will_v be_v very_o clear_a that_o the_o benefit_n which_o result_v from_o this_o diversion_n or_o vent_n be_v not_o so_o great_a as_o be_v universal_o presume_v i_o say_v it_o be_v not_o so_o great_a as_o be_v presume_v because_o though_o it_o be_v grant_v for_o true_a that_o the_o water_n of_o the_o main_a po_n abate_v at_o the_o begin_n of_o the_o vent_n yet_o this_o benefit_n happen_v to_o be_v but_o temporary_a and_o for_o a_o few_o hour_n if_o the_o rise_n of_o po_n and_o the_o danger_n of_o break_v forth_o be_v of_o short_a duration_n as_o it_o ordinary_o befall_v in_o the_o overflowing_n of_o torrent_n in_o such_o a_o case_n the_o profit_n of_o the_o vent_n will_v be_v of_o some_o esteem_n but_o because_o the_o swell_n of_o po_n continue_v for_o thirty_o or_o sometime_o for_o forty_o day_n therefore_o the_o gain_n which_o result_v from_o the_o vent_n prove_v to_o be_v inconsiderable_a it_o remain_v now_o to_o consider_v the_o notable_a harm_n which_o follow_v the_o say_a sluice_n or_o vent_n that_o so_o reflection_n be_v make_v and_o the_o profit_n and_o the_o detriment_n compare_v one_o may_v right_o judge_v and_o choose_v that_o which_o shall_v be_v most_o convenient_a the_o first_o prejudice_n therefore_o which_o arise_v from_o this_o vent_n or_o sluice_n be_v that_o the_o channel_n of_o ferara_n primaro_n and_o volana_n fill_v with_o water_n all_o those_o part_n from_o bondeno_n to_o the_o sea_n side_n be_v alarm_v and_o endanger_v thereby_o second_o the_o water_n of_o the_o po_n of_o primaro_n have_v free_a ingress_n into_o the_o upper_a valley_n they_o fill_v they_o to_o the_o great_a damage_n of_o the_o field_n adjacent_a and_o obstruct_v the_o course_n of_o the_o ordinary_a trench_n in_o the_o same_o valley_n insomuch_o that_o all_o the_o care_n cost_n and_o labour_n about_o the_o drain_n and_o free_v the_o upper_a valley_n from_o water_n will_v also_o become_v vain_a and_o ineffectual_a three_o i_o consider_v that_o these_o water_n of_o the_o po_n of_o ferara_n be_v pass_v downward_o towards_o the_o sea_n at_o the_o time_n 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in_o the_o low_a part_n namely_o below_o the_o breach_n there_o be_v beget_v in_o the_o channel_n of_o the_o river_n a_o certain_a ridge_n or_o shelf_n that_o be_v the_o bottom_n of_o the_o river_n be_v raise_v as_o be_v sufficient_o manifest_a by_o experience_n and_o thus_o just_a in_o the_o same_o manner_n cut_v the_o bank_n at_o bondeno_n there_o be_v at_o it_o be_v a_o breach_n make_v from_o which_o follow_v the_o rise_n in_o the_o low_a part_n of_o the_o main_a po_n be_v past_o the_o mouth_n of_o pamaro_n which_o thing_n how_o pernicious_a it_o be_v let_v any_o one_o judge_n that_o understand_v these_o matter_n and_o therefore_o both_o for_o the_o small_a benefit_n and_o so_o many_o harm_n that_o ensue_v from_o maintain_v this_o diversion_n i_o shall_v think_v it_o be_v more_o sound_a advice_n to_o keep_v that_o bank_n always_o whole_a at_o bondeno_n or_o in_o any_o other_o convenient_a place_n and_o not_o to_o permit_v that_o the_o water_n of_o the_o grand_a po_n shall_v ever_o come_v near_o to_o ferara_n corollary_n fourteen_o in_o the_o grand_a river_n which_o fall_v into_o the_o sea_n as_o here_o in_o italy_n po_n adige_n artesia_n and_o arno_n which_o be_v arm_v with_o bank_n against_o their_o excrescency_n it_o be_v observe_v that_o far_o from_o the_o sea_n they_o need_v bank_n of_o a_o notable_a height_n which_o height_n go_v afterward_o by_o degree_n diminish_v the_o more_o it_o approach_v to_o the_o seacoast_n in_o such_o sort_n that_o the_o po_n distant_a from_o the_o sea_n about_o fifty_o or_o sixty_o mile_n at_o ferara_n shall_v have_v bank_n that_o be_v above_o twenty_o foot_n high_o than_o the_o ordinary_a water-mark_n but_o ten_o or_o twelve_o mile_n from_o the_o sea_n the_o bank_n be_v not_o twelve_o foot_n high_o than_o the_o say_v ordinary_a water-mark_n though_o the_o breadth_n of_o the_o river_n be_v the_o same_o so_o that_o the_o excrescence_n of_o the_o same_o innundation_n happen_v to_o be_v far_o great_a in_o measure_n remote_a from_o the_o sea_n then_o near_o and_o yet_o it_o shall_v seem_v that_o the_o same_o quantity_n of_o water_n pass_v by_o every_o place_n the_o river_n shall_v need_v to_o have_v the_o same_o altitude_n of_o bank_n in_o all_o place_n but_o we_o by_o our_o principle_n and_o fundamental_o may_v be_v able_a to_o render_v the_o reason_n of_o that_o effect_n and_o say_v that_o that_o excess_n of_o quantity_n of_o water_n above_o the_o ordinary_a water_n go_v always_o acquire_v great_a velocity_n the_o near_a it_o approach_v the_o sea_n and_o therefore_o decrease_v in_o measure_n and_o consequent_o in_o height_n and_o this_o perhaps_o may_v have_v be_v the_o cause_n in_o great_a part_n why_o the_o tiber_n in_o the_o innundation_n anno_fw-la 1578._o issue_v not_o forth_o of_o its_o channel_n below_o rome_n towards_o the_o sea_n corollary_n xv._n from_o the_o same_o doctrine_n may_v be_v render_v a_o most_o manifest_a reason_n why_o the_o fall_a water_n go_v lessen_v in_o their_o descent_n so_o that_o the_o same_o fall_a water_n measure_v at_o the_o begin_n of_o its_o fall_n be_v great_a and_o big_a and_o afterward_o by_o degree_n lessen_v in_o measure_n the_o more_o it_o be_v remote_a from_o the_o begin_n of_o the_o fall_n which_o depend_v on_o no_o other_o than_o on_o the_o acquisition_n which_o it_o successive_o make_v of_o great_a velocity_n it_o be_v a_o most_o familiar_a conclusion_n among_o philosopher_n that_o grave_a body_n fall_v the_o more_o they_o remove_v from_o the_o begin_n of_o their_o motion_n the_o more_o they_o acquire_v of_o swiftness_n and_o therefore_o the_o water_n as_o a_o grave_a body_n falling_z gradual_o velocitates_fw-la and_o therefore_o decrease_v in_o measure_n and_o lessen_v corollary_n xvi_o and_o on_o the_o contrary_a the_o spirting_n of_o a_o fountain_n of_o water_n which_o spring_n on_o high_a work_v a_o contrary_a effect_n namely_o in_o the_o beginning_n they_o be_v small_a and_o afterward_o become_v great_a and_o big_a and_o the_o reason_n be_v most_o manifest_a because_o in_o the_o beginning_n they_o be_v very_o swift_a and_o afterward_o gradual_o relent_v their_o impetuosity_n and_o motion_n so_o that_o in_o the_o begin_n of_o the_o excursion_n that_o they_o make_v they_o ought_v to_o be_v small_a and_o afterward_o to_o grow_v big_a as_o in_o the_o effect_n be_v see_v appendix_n i._o into_o the_o error_n of_o not_o consider_v how_o much_o the_o different_a velocity_n of_o the_o same_o run_a water_n in_o several_a place_n of_o its_o current_n be_v able_a to_o change_v the_o measure_n of_o the_o same_o water_n and_o to_o make_v it_o great_a or_o less_o i_o think_v if_o i_o be_v not_o deceive_v that_o ginlio_n frontino_n a_o noble_a ancient_a writer_n may_v have_v fall_v in_o the_o second_o book_n which_o he_o write_v of_o the_o aqueduct_n of_o the_o city_n of_o rome_n whilst_o find_v the_o measure_n of_o the_o water_n water_n commentariis_fw-la less_o than_o it_o be_v in_o erogatione_fw-la 1263._o quinary_n he_o think_v that_o so_o much_o difference_n may_v proceed_v from_o the_o negligence_n of_o the_o measure_n and_o when_o afterward_o with_o his_o own_o industry_n he_o measure_v the_o same_o water_n at_o the_o begin_n of_o the_o aqueduct_n find_v it_o near_o 10000_o quinary_n big_a than_o it_o be_v in_o commentariis_fw-la he_o judge_v that_o the_o overplus_n be_v imbezile_v by_o minister_n and_o partaker_n which_o in_o part_n may_v be_v so_o for_o it_o be_v but_o too_o true_a that_o the_o public_a be_v almost_o always_o defraud_v yet_o nevertheless_o i_o very_o believe_v withal_o that_o beside_o the_o fraud_n of_o these_o officer_n the_o velocity_n of_o the_o water_n in_o the_o place_n wherein_o frontino_n measure_v it_o may_v be_v different_a from_o those_o velocity_n which_o be_v find_v in_o other_o place_n before_o measure_v by_o other_o and_o therefore_o the_o measure_n of_o the_o water_n may_v yea_o ought_v necessary_o to_o be_v different_a it_o have_v be_v by_o we_o demonstrate_v that_o the_o measure_n of_o the_o same_o run_a water_n have_v reciprocal_a proportion_n to_o their_o velocity_n which_o frontino_n not_o well_o consider_v and_o find_v the_o water_n in_o commentariis_fw-la 12755._o quinary_n in_o erogatione_fw-la 14018_o and_o in_o his_o own_o measure_n ad_fw-la capita_fw-la ductuum_fw-la at_o the_o head_n of_o the_o fountain_n 22755._o quinary_n or_o thereabouts_o he_o think_v that_o in_o all_o these_o place_n there_o past_a different_a quantity_n of_o water_n namely_o great_a at_o the_o fountain_n head_n than_o that_o which_o be_v in_o erogatione_fw-la and_o this_o he_o judge_v great_a than_o that_o which_o be_v in_o commentariis_fw-la appendix_n ii_o a_o like_a mistake_n chance_v late_o in_o the_o aqueduct_v of_o acqua-paola_n which_o water_n shall_v be_v 2000_o inch_n and_o so_o many_o effective_o aught_o to_o be_v allow_v and_o it_o have_v be_v give_v in_o so_o to_o be_v by_o the_o signor_n of_o bracciano_n to_o the_o apostolic-chamber_n and_o there_o be_v a_o measure_n thereof_o make_v at_o the_o begin_n of_o the_o aqueduct_v which_o measure_n prove_v afterward_o much_o less_o and_o short_a consider_v and_o take_v in_o rome_n and_o thence_o follow_v discontent_n and_o great_a disorder_n and_o all_o because_o this_o property_n of_o running-water_n of_o increase_v in_o measure_n where_o the_o velocity_n decrease_v and_o of_o diminish_v in_o measure_n where_o the_o velocity_n augment_v be_v not_o look_v into_o appendix_n iii_o a_o like_a error_n in_o my_o judgement_n have_v be_v commit_v by_o all_o those_o learned_a man_n which_o to_o prevent_v the_o diversion_n of_o the_o reno_n of_o bologna_n into_o po_n by_o the_o channel_n through_o which_o it_o at_o present_a run_v judge_v that_o the_o reno_n be_v in_o its_o great_a excrescence_n about_o 2000_o foot_n and_o the_o po_n be_v near_o 1000_o foot_n broad_a they_o judge_v i_o say_v that_o let_v the_o reno_n into_o po_n it_o will_v have_v raise_v the_o water_n of_o po_n two_o foot_n from_o which_o rise_n they_o conclude_v afterward_o most_o exorbitant_a disorder_n either_o of_o extraordinary_a inundation_n or_o else_o of_o immense_a and_o intolerable_a expense_n to_o the_o people_n in_o raise_v the_o bank_n of_o po_n and_o reno_n and_o with_o such_o like_a weakness_n often_o vain_o disturb_v the_o mind_n of_o the_o person_n concern_v but_o now_o from_o the_o thing_n demonstrare_v it_o be_v manifest_a that_o the_o measure_n of_o the_o reno_n in_o reno_n will_v be_v different_a from_o the_o measure_n of_o reno_n in_o po_n in_o case_n that_o the_o velocity_n of_o the_o reno_n in_o po_n shall_v differ_v from_o the_o velocity_n of_o reno_n in_o reno_n as_o be_v more_o exact_o determine_v in_o the_o four_o proposition_n appendix_n iu._n no_o less_o likewise_o be_v those_o ingeneer_n and_o artist_n deceive_v that_o have_v affirm_v that_o let_v the_o reno_n into_o po_n there_o will_v be_v
the_o rule_n mention_v above_o in_o the_o first_o proposition_n that_o the_o quantity_n of_o the_o water_n that_o run_v through_o the_o chanellet_n be_v v_o g._n a_o hundred_o barrel_n in_o the_o space_n of_o 15_o second_o minute_n of_o a_o hour_n it_o be_v manifest_a that_o the_o water_n which_o run_v through_o the_o great_a channel_n in_o the_o say_a time_n of_o 35_o min._n sec._n shall_v be_v about_o 600_o barrel_n the_o same_o operation_n perform_v another_o way_n and_o because_o very_o often_o in_o apply_v the_o theory_n to_o practise_v it_o happen_v that_o all_o the_o necessary_a particular_n in_o the_o theory_n can_v so_o easy_o be_v put_v in_o execution_n therefore_o we_o will_v here_o add_v another_o way_n of_o perform_v the_o same_o problem_n if_o it_o shall_v chance_v to_o happen_v that_o the_o chanellet_n can_v not_o commodious_o be_v divert_v from_o the_o great_a channel_n but_o that_o it_o be_v easy_a for_o the_o water_n of_o another_o small_a channel_n to_o be_v bring_v into_o the_o great_a channel_n which_o water_n of_o the_o small_a channel_n may_v be_v easy_o measure_v as_o have_v be_v show_v in_o the_o first_o problem_n or_o in_o case_n that_o there_o do_v fall_v into_o a_o great_a channel_n a_o lesser_a channel_n that_o may_v be_v divert_v and_o measure_v therefore_o i_o say_v in_o the_o first_o case_n if_o we_o will_v measure_v the_o quantity_n of_o the_o water_n that_o run_v in_o a_o certain_a time_n through_o the_o great_a channel_n into_o which_o another_o lesser_a channel_n that_o be_v measurable_a may_v be_v bring_v we_o must_v first_o exact_o measure_v the_o chanellet_n and_o then_o observe_v the_o quick_a height_n of_o the_o great_a channel_n before_o the_o introduction_n of_o the_o lesser_a and_o have_v bring_v in_o the_o say_a chanellet_n we_o must_v agnin_n find_v the_o proportion_n that_o the_o water_n of_o the_o chanellet_n have_v to_o all_o the_o water_n of_o the_o great_a channel_n for_o these_o term_n of_o the_o proportion_n be_v know_v as_o also_o the_o quantity_n of_o the_o water_n of_o the_o chanellet_n we_o shall_v also_o come_v to_o know_v the_o quantity_n of_o the_o water_n that_o run_v through_o the_o great_a channel_n it_o be_v likewise_o manifest_a that_o we_o shall_v obtain_v our_o intent_n if_o the_o case_n be_v that_o there_o enter_v into_o the_o great_a channel_n another_o lesser_a channel_n that_o be_v measurable_a and_o that_o may_v be_v divert_v consideration_n it_o will_v be_v necessary_a to_o make_v use_n of_o this_o doctrine_n in_o the_o distribution_n of_o the_o water_n that_o be_v employ_v to_o overflow_v the_o field_n as_o be_v use_v in_o the_o brescian_a cremonese_n bergamase_v lodigian_a milanese_n territory_n and_o many_o other_o place_n where_o very_o great_a suit_n and_o difference_n arise_v which_o not_o be_v to_o be_v determine_v with_o intelligible_a reason_n come_v oftentimes_o to_o be_v decide_v by_o force_n of_o arm_n and_o instead_o of_o flow_v their_o ground_n with_o water_n they_o cruel_o flow_v they_o with_o the_o shed_n of_o humane_a blood_n impious_o invert_v the_o course_n of_o peace_n and_o justice_n sow_v such_o disorder_n and_o feud_n as_o that_o they_o be_v sometime_o accompany_v with_o the_o ruin_n of_o whole_a city_n or_o else_o unprofitable_o charge_v they_o with_o vain_a and_o sometime_o prejudicial_a expense_n propos_fw-fr iv._o theor._n ii_o if_o a_o river_n increase_v in_o quick_a height_n the_o quantity_n of_o water_n which_o the_o river_n discharge_v after_o the_o increase_n have_v the_o proportion_n compound_v of_o the_o proportion_n of_o the_o quick_a height_n to_o the_o quick_a height_n and_o of_o the_o velocity_n to_o the_o velocity_n let_v there_o be_v a_o river_n which_o whilst_o it_o be_v low_a run_v through_o the_o regulator_n df_n with_o the_o quick_a height_n ab_fw-la and_o afterward_o let_v a_o flood_n come_v and_o then_o let_v it_o run_v with_o the_o height_n db_n i_o say_v that_o the_o quantity_n of_o the_o water_n that_o be_v discharge_v through_o df_n to_o that_o which_o discharge_v through_o of_o have_v the_o proportion_n compound_v of_o the_o proportion_n of_o the_o velocity_n through_o df_n to_o the_o velocity_n through_o of_o and_o of_o the_o height_n db_n to_o the_o height_n ab_fw-la as_o the_o velocity_n through_o df_n be_v to_o the_o velocity_n through_o of_o so_o let_v the_o line_n r_o be_v to_o the_o line_n s_o and_o as_o the_o height_n db_n be_v to_o the_o height_n ab_fw-la so_o let_v the_o line_n s_o be_v to_o the_o line_n t._n and_o let_v a_o section_n be_v suppose_v lmn_n equal_a to_o the_o section_n df_n in_o height_n and_o length_n but_o let_v it_o be_v in_o velocity_n equal_a to_o the_o section_n af._n therefore_o the_o quantity_n of_o the_o water_n that_o run_v through_o df_n to_o that_o which_o run_v through_o ln_o shall_v be_v as_o the_o velocity_n through_o df_n to_o the_o velocity_n of_o ln_o that_o be_v to_o the_o velocity_n through_o ln_o that_o be_v to_o the_o velocity_n through_o af._n therefore_o the_o quantity_n of_o water_n which_o run_v through_o df_n to_o that_o which_o pass_v through_o ln_o shall_v have_v the_o proportion_n that_o r_o have_v to_o saint_n but_o the_o quantity_n of_o the_o water_n that_o run_v through_o ln_o to_o that_o which_o run_v through_o of_o the_o section_n be_v equal_o swift_a shall_v have_v the_o proportion_n that_o the_o section_n ln_o have_v to_o the_o section_n of_o that_o be_v that_o the_o height_n bd_o have_v to_o the_o height_n basilius_n that_o be_v that_o saint_n have_v to_o t._n therefore_o by_o equal_a proportion_n the_o quantity_n of_o the_o water_n which_o run_v by_o df_n to_o that_o which_o run_v by_o of_o shall_v have_v the_o proportion_n of_o r_o to_o t_n that_o be_v shall_v be_v compound_v of_o the_o proportion_n of_o the_o height_n db_n to_o the_o height_n ab_fw-la and_o of_o the_o velocity_n through_o df_n to_o the_o velocity_n through_o af._n and_o therefore_o if_o a_o river_n increase_v in_o quick_a height_n the_o quantity_n of_o the_o water_n that_o run_v after_o the_o increase_n to_o that_o which_o run_v before_o the_o increase_n have_v the_o proportion_n compound_v etc._n etc._n which_o be_v to_o be_v demonstrate_v corollary_n i._n hence_o it_o follow_v that_o we_o have_v show_v that_o the_o quantity_n of_o the_o water_n which_o run_v whilst_o the_o river_n be_v high_a to_o that_o which_o run_v whilst_o it_o be_v low_a have_v the_o proportion_n compound_v of_o the_o velocity_n to_o the_o velocity_n and_o of_o the_o height_n to_o the_o height_n and_o it_o have_v be_v demonstrate_v that_o the_o velocity_n to_o the_o velocity_n be_v as_o the_o height_n to_o the_o height_n it_o follow_v i_o say_v that_o the_o quantity_n of_o the_o water_n that_o run_v whilst_o the_o river_n be_v high_a to_o that_o which_o run_v whilst_o it_o be_v low_a have_v duplicate_v proportion_n of_o the_o height_n to_o the_o height_n that_o be_v the_o proportion_n that_o the_o square_n of_o the_o height_n have_v corollary_n ii_o upon_o which_o thing_n depend_v the_o reason_n of_o that_o which_o i_o have_v say_v in_o my_o second_o consideration_n that_o if_o by_o the_o diversion_n of59._o of_o the_o water_n that_o enter_v by_o the_o river_n into_o the_o moor_n or_o fen_n the_o water_n be_v abate_v such_o a_o measure_n that_o same_o shall_v be_v only_o one_o three_o of_o its_o whole_a height_n but_o moreover_o divert_v the_o 49_o it_o shall_v abate_v two_o other_o three_o a_o most_o principal_a point_n and_o such_o that_o it_o be_v not_o have_v be_v well_o understand_v have_v cause_v very_o great_a disorder_n and_o there_o will_v now_o more_o than_o ever_o follow_v extreme_a damage_n if_o one_o shall_v put_v in_o execution_n the_o diversion_n of_o the_o sile_z and_o other_o river_n and_o it_o be_v manifest_a that_o in_o the_o same_o manner_n wherewith_o it_o have_v be_v demonstrate_v that_o the_o quantity_n of_o the_o water_n increase_v quadruple_a the_o height_n will_v increase_v only_o double_a and_o the_o quantity_n increase_v nonuple_n the_o height_n increase_v triple_a so_o that_o by_o add_v to_o unit_v all_o the_o odd_a number_n according_a to_o their_o series_n the_o height_n increase_v according_a to_o the_o natural_a progression_n of_o all_o the_o number_n from_o unit_n as_o for_o example_n there_o pass_v through_o a_o regulator_n such_o a_o certain_a quantity_n of_o water_n in_o one_o time_n add_v three_o of_o those_o measure_n the_o quick_a height_n be_v two_o of_o those_o part_n which_o at_o first_o be_v one_o and_o continue_v to_o add_v five_o of_o those_o say_a measure_n the_o height_n be_v three_o of_o those_o part_n which_o at_o first_o be_v one_o and_o thus_o add_v seven_o and_o then_o nine_o and_o then_o 11._o and_o then_o 13_o etc._n etc._n the_o height_n shall_v be_v 4._o then_o 5_o than_o 6._o then_o 7_o
velocity_n convenient_a to_o the_o circular_a motion_n betwixt_o rest_n and_o any_o assign_a degree_n of_o velocity_n infinite_a degree_n of_o less_o velocity_n interpose_v nature_n do_v not_o immediate_o confer_v a_o determinate_a degree_n of_o velocity_n howbeit_o she_o can_v the_o movable_a depart_n from_o rest_n pass_v through_o all_o degree_n of_o velocity_n without_o stay_v in_o any_o the_o ponderous_a mover_n descend_v acquire_v impetus_fw-la sufficient_a to_o recarry_v it_o to_o the_o like_a height_n the_o impetuosity_n of_o moveable_n equal_o approach_v to_o the_o centre_n be_v equal_a upon_o a_o horizontall_a plane_n the_o movable_a lie_v still_o the_o velocity_n by_o the_o incline_a plane_n equal_a to_o the_o velocity_n by_o the_o perpendicular_a and_o the_o motion_n by_o the_o perpendicular_a swift_o than_o by_o the_o inclination_n velocity_n be_v say_v to_o be_v equal_a when_o the_o space_n pass_v be_v proportionate_a to_o their_o time_n the_o circular_a motion_n be_v never_o acquire_v natural_o without_o right_a motion_n precede_v it_o circular_a motion_n perpetual_o uniform_a the_o magnitude_n of_o the_o orb_n and_o the_o velocity_n of_o the_o motion_n of_o the_o planet_n answer_v proportionable_o as_o if_o descend_v from_o the_o same_o place_n finite_a and_o terminate_v circular_a motion_n disorder_v not_o the_o part_n of_o the_o world_n in_o the_o circular_a motion_n every_o point_n in_o the_o circumference_n be_v the_o begin_n and_o end_n circular_a motion_n only_o be_v uniform_a circular_a motion_n may_v be_v continue_v perpetual_o right_o motion_n can_v natural_o be_v perpetual_a right_o motion_n assign_v to_o natural_a body_n to_o reduce_v they_o to_o perfect_a order_n when_o remove_v from_o their_o place_n rest_v only_o and_o circular_a motion_n be_v apt_a to_o conserve_v order_n sensible_n experiment_n be_v to_o be_v prefer_v before_o humane_a argumentation_n he_o who_o deny_v sense_n deserve_v to_o be_v deprive_v of_o it_o sense_n show_v 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quò_fw-la humiliores_fw-la tardiùs_fw-la i._n e._n why_o be_v the_o high_a the_o swift_a and_o the_o low_a the_o ●lower_n salv_n because_o that_o in_o a_o sphere_n or_o circle_n that_o turn_v about_o upon_o its_o own_o centre_n the_o remote_a part_n describe_v great_a circuit_n and_o the_o part_n near_o at_o hand_n describe_v lesser_a in_o the_o same_o time_n simp_n quare_fw-la quae_fw-la aequinoctiali_fw-la propriores_fw-la in_fw-la majori_fw-la quae_fw-la remotiores_fw-la in_fw-la minori_fw-la circulo_fw-la feruntur_fw-la scilicet_fw-la why_o be_v those_o near_o the_o aequinoctial_a carry_v about_o in_o a_o great_a circle_n and_o those_o which_o be_v remote_a in_o a_o lesser_a salv_n to_o imitate_v the_o starry_a sphere_n in_o which_o those_o near_a to_o the_o aequinoctial_a move_v in_o great_a circle_n than_o the_o more_o remote_a simp_n quarè_v pila_fw-la eadem_fw-la sub_fw-la aequinoctiali_fw-la tota_fw-la circa_fw-la centrum_fw-la terrae_fw-la ambitu_fw-la maximo_fw-la celeritate_fw-la incredibili_fw-la sub_fw-la polo_n verò_fw-la circa_fw-la centrum_fw-la proprium_fw-la gyro_fw-la nullo_n tarditate_fw-la supremà_fw-la volveretur_fw-la that_o be_v why_o be_v the_o same_o ball_n under_o the_o aequinoctial_a whole_o turn_v round_o the_o centre_n of_o the_o earth_n in_o the_o great_a circumference_n with_o a_o incredible_a celerity_n but_o under_o the_o pole_n about_o its_o own_o centre_n in_o no_o circuit_n but_o with_o the_o ultimate_a degree_n of_o tardity_n salv_n to_o imitate_v the_o star_n of_o the_o firmament_n that_o will_v do_v the_o like_a if_o they_o have_v the_o diurnal_a motion_n simp_n quare_fw-la eadem_fw-la res_fw-la pila_fw-la v._n g._n plumbea_fw-la si_fw-la semel_fw-la terram_fw-la circuivit_fw-la descripto_fw-la circulo_fw-la maximo_fw-la eandem_fw-la ubique_fw-la non_fw-la circummigret_n secundùm_fw-la circulum_fw-la maximum_fw-la sed_fw-la translata_fw-la extra_fw-la aequinoctialem_fw-la in_o circulis_fw-la minoribus_fw-la agetur_fw-la which_o speak_v thus_o why_o do_v not_o the_o same_o thing_n as_o for_o example_n a_o ball_n of_o lead_n turn_v round_o every_o where_o according_a to_o the_o same_o great_a circle_n if_o once_o describe_v a_o great_a circle_n it_o have_v encompass_v the_o earth_n but_o be_v remove_v from_o the_o
without_o those_o capillious_a ray_n nor_o can_v this_o their_o inadvertency_n be_v excuse_v in_o regard_n that_o it_o be_v in_o their_o power_n to_o have_v behold_v they_o at_o their_o pleasure_n without_o those_o tress_n which_o be_v do_v by_o look_v upon_o they_o at_o their_o first_o appearance_n in_o the_o evening_n inexcusable_a or_o their_o last_o occultation_n in_o the_o come_n on_o of_o day_n and_o if_o none_o of_o the_o rest_n yet_o venus_n which_o oft_o time_n be_v see_v at_o noon_n day_n so_o small_a that_o one_o must_v sharpen_v the_o sight_n in_o discern_v it_o and_o again_o in_o the_o follow_a night_n seem_v a_o great_a flake_n of_o light_n may_v advertise_v they_o of_o their_o fallacy_n for_o i_o will_v not_o believe_v that_o they_o think_v the_o true_a discus_fw-la to_o be_v that_o which_o be_v see_v in_o the_o obscure_a darkness_n and_o not_o that_o which_o be_v discern_v in_o the_o luminous_a medium_fw-la for_o our_o light_n which_o see_v by_o night_n afar_o off_o appear_v great_a and_o near_o at_o hand_n show_v their_o true_a lustre_n to_o be_v terminate_v and_o small_a may_v have_v easy_o have_v make_v they_o cautious_a nay_o if_o i_o may_v free_o speak_v my_o thought_n i_o absolute_o believe_v that_o none_o of_o they_o no_o not_o tycho_n himself_o so_o accurate_a in_o handle_v astronomical_a instrument_n and_o that_o so_o great_a and_o accurate_a without_o spare_v very_o great_a cost_n in_o their_o construction_n do_v ever_o go_v about_o to_o take_v and_o measure_v the_o apparent_a diameter_n of_o any_o star_n the_o sun_n and_o moon_n except_v but_o i_o think_v that_o arbitrary_o and_o as_o we_o say_v with_o the_o eye_n some_o one_o of_o the_o more_o ancient_a of_o they_o pronounce_v the_o thing_n to_o be_v so_o and_o so_o and_o that_o all_o that_o follow_v he_o afterward_o without_o more_o ado_n keep_v close_o to_o what_o the_o first_o have_v say_v for_o if_o any_o one_o of_o they_o have_v apply_v himself_o to_o have_v make_v some_o new_a proof_n of_o the_o same_o he_o will_v doubtless_o have_v discover_v the_o fraud_n sagr._fw-la but_o if_o they_o want_v the_o telescope_n and_o you_o have_v already_o say_v that_o our_o friend_n with_o that_o same_o instrument_n come_v to_o the_o knowledge_n of_o the_o truth_n they_o ought_v to_o be_v excuse_v and_o not_o accuse_v of_o ignorance_n salv_n this_o will_v hold_v good_a if_o without_o the_o telescope_n the_o business_n can_v not_o be_v effect_v it_o be_v true_a that_o this_o instrument_n by_o show_v the_o discus_fw-la of_o the_o star_n naked_a and_o magnify_v a_o hundred_o or_o a_o thousand_o time_n render_v the_o operation_n much_o more_o easy_a but_o the_o same_o thing_n may_v be_v do_v although_o not_o altogether_o so_o exact_o without_o the_o instrument_n and_o i_o have_v many_o time_n do_v the_o same_o and_o my_o method_n therein_o be_v this_o i_o have_v cause_v a_o rope_n to_o be_v hang_v towards_o some_o star_n star_n and_o i_o have_v make_v use_n of_o the_o constellation_n call_v the_o harp_n which_o rise_v between_o the_o north_n and_o northwest_n north-east_n and_o then_o by_o go_v towards_o and_o from_o the_o say_a rope_n interpose_v between_o i_o and_o the_o star_n i_o have_v find_v the_o place_n from_o whence_o the_o thickness_n of_o the_o rope_n have_v just_o hide_v the_o star_n from_o i_o this_o do_v i_o have_v take_v the_o distance_n from_o the_o eye_n to_o the_o rope_n which_o be_v one_o of_o the_o side_n include_v the_o angle_n that_o be_v compose_v in_o the_o eye_n and_o by_o which_o insist_v upon_o the_o thickness_n of_o the_o rope_n and_o which_o be_v like_a yea_o the_o same_o with_o the_o angle_n in_o the_o starry_a sphere_n that_o insist_v upon_o the_o diameter_n of_o the_o star_n and_o by_o the_o proportion_n of_o the_o rope_n thickness_n to_o the_o distance_n from_o the_o eye_n to_o the_o rope_n by_o the_o table_n of_o arch_n and_o chord_n i_o have_v immediate_o find_v the_o quantity_n of_o the_o angle_n use_v all_o the_o while_n the_o wont_a caution_n that_o be_v observe_v in_o take_v angle_n so_o acute_a not_o to_o form_v the_o concourse_n of_o the_o visive_a ray_n in_o the_o centre_n of_o the_o eye_n where_o they_o be_v only_o refract_v but_o beyond_o the_o eye_n where_o real_o the_o pupil_n greatness_n make_v they_o to_o concur_v sagr._fw-la i_o apprehend_v this_o your_o cautelous_a procedure_n albeit_o i_o have_v a_o kind_n of_o haesitancy_n touch_v the_o same_o but_o that_o which_o most_o puzzle_v i_o be_v that_o in_o this_o operation_n if_o it_o be_v make_v in_o the_o dark_a of_o night_n methinks_v that_o you_o measure_v the_o diameter_n of_o the_o irradiate_v discus_fw-la and_o not_o the_o true_a and_o naked_a face_n of_o the_o star_n salv_n not_o so_o sir_n for_o the_o rope_n in_o cover_v the_o naked_a body_n of_o the_o star_n take_v away_o the_o ray_n which_o belong_v not_o to_o it_o but_o to_o our_o eye_n of_o which_o it_o be_v deprive_v so_o soon_o as_o the_o true_a discus_fw-la thereof_o be_v hide_v and_o in_o make_v the_o observation_n you_o shall_v see_v how_o unexpected_o a_o little_a cord_n will_v cover_v that_o reasonable_a big_a body_n of_o light_n which_o seem_v impossible_a to_o be_v hide_v unless_o it_o be_v with_o a_o much_o broad_a screen_v to_o measure_n in_o the_o next_o place_n and_o exact_o to_o find_v out_o how_o many_o of_o those_o thickness_n of_o the_o rope_n interpose_v in_o the_o distance_n between_o the_o say_a rope_n and_o the_o eye_n i_o take_v not_o only_o one_o diameter_n of_o the_o rope_n but_o lay_v many_o piece_n of_o the_o same_o together_o upon_o a_o table_n so_o that_o they_o touch_v i_o take_v with_o a_o pair_n of_o compass_n the_o whole_a space_n occupy_v by_o fifteen_o or_o twenty_o of_o they_o and_o with_o that_o measure_n i_o commensurate_a the_o distance_n before_o with_o another_o small_a cord_n take_v from_o the_o rope_n to_o the_o concourse_n of_o the_o visive_a ray_n and_o with_o this_o sufficiently-exact_a operation_n i_o 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the_o great_a or_o lesser_a magnitude_n of_o the_o object_n that_o be_v behold_v as_o because_o that_o in_o observe_v object_n of_o the_o same_o bigness_n it_o seem_v to_o i_o that_o the_o concourse_n of_o the_o ray_n for_o certain_a other_o respect_v aught_o to_o be_v make_v more_o and_o less_o remote_a from_o the_o eye_n salv_n i_o see_v already_o whither_o the_o apprehension_n of_o sagredus_fw-la a_o most_o diligent_a observer_n of_o nature_n secret_n tend_v and_o i_o will_v lay_v any_o wager_n contract_v that_o among_o the_o thousand_o that_o have_v observe_v cat_n to_o contract_n and_o enlarge_v the_o pupil_n of_o their_o eye_n very_o much_o there_o be_v not_o two_o nor_o haply_o one_o that_o have_v observe_v the_o like_a effect_n to_o be_v wrought_v by_o the_o pupil_n of_o man_n in_o see_v whilst_o the_o medium_n be_v much_o or_o little_a illumine_v and_o that_o in_o the_o open_a light_n the_o circlet_n of_o the_o pupil_n diminish_v considerable_o so_o that_o in_o look_v upon_o the_o face_n or_o discus_fw-la of_o the_o sun_n it_o be_v reduce_v to_o a_o smallnesse_n lesser_a than_o a_o grain_n of_o seed_n panic_n and_o in_o behold_v object_n that_o do_v not_o shine_v and_o be_v in_o a_o less_o luminous_a medium_n it_o be_v enlarge_v to_o the_o bigness_n of_o a_o lintel_n or_o more_o and_o in_o sum_n this_o expansion_n and_o contraction_n differ_v in_o more_o than_o decuple_n proportion_n from_o whence_o it_o be_v manifest_a that_o when_o the_o pupil_n be_v much_o dilate_v it_o be_v necessary_a that_o the_o angle_n of_o the_o ray_n concourse_n be_v more_o remote_a from_o the_o eye_n which_o happen_v in_o behold_v object_n little_o luminate_v this_o be_v a_o doctrine_n which_o sagredus_fw-la have_v just_o now_o give_v i_o the_o hint_n of_o whereby_o if_o we_o be_v to_o make_v